Controlled-Accuracy Approximation of Nonlinear Functions for Soft Computing Applications: A High Performance Co-proccessor for Intelligent Embedded Systems

Intelligent embedded systems can be found everywhere in a variety of innovative applications. The main challenge consists in developing small-size single-chip embedded systems with low power consumption, capable of processing data and intelligent algorithms with the required speed. These key issues are normally carefully analyzed during the design process of embedded systems with the aim of meeting the required specifications. However, the problem of accuracy is hardly ever explored at early stages of the design flow, even though too low accuracy could limit digital hardware performance in a crucial way. This piece of work proposes a controlled accuracy approximation scheme of nonlinear functions based on Taylor´s Theorem and the Lagrange form of the remainder. A hardware co-processor based on a Field programmable Gate Array (FPGA) is developed. The co-processor is suitable for efficient computation of nonlinear functions involved in typical soft computing techniques such as: activation functions (neural networks), membership functions (fuzzy systems), or kernel functions (support vector machines). The method is applied to the development of an intelligent embedded system for a smart scenario. Experimental results are provided for both online training and feed-forward computation of a single-layer feed-forward neural network.